{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.uniform(-3, 3, size=100)\n",
    "X = x.reshape(-1, 1)\n",
    "y = 0.5 * x**2 + x + 2 + np.random.normal(0, 1, size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly = PolynomialFeatures(degree=2)  # 指定添加2次幂\n",
    "poly.fit(X)\n",
    "X2 = poly.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 3)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  2.01449669,  4.0581969 ],\n",
       "       [ 1.        , -1.85707185,  3.44871584],\n",
       "       [ 1.        ,  0.26737671,  0.0714903 ],\n",
       "       [ 1.        , -0.76480918,  0.58493309],\n",
       "       [ 1.        ,  1.94309225,  3.77560748]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X2[:5,:]  # 第一列为X的0次方， 第二列是X的1次方， 第三列是X的2次方"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.01449669],\n",
       "       [-1.85707185],\n",
       "       [ 0.26737671],\n",
       "       [-0.76480918],\n",
       "       [ 1.94309225]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:5,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X2, y)\n",
    "X2_predict = lin_reg.predict(X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f15c1167d90>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(np.sort(x), X2_predict[np.argsort(x)], color='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.9347289 , 0.43130998])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2575744429703937"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 关于PolynomialFeature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.arange(1, 11).reshape(-1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 2)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2],\n",
       "       [ 3,  4],\n",
       "       [ 5,  6],\n",
       "       [ 7,  8],\n",
       "       [ 9, 10]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(degree=2)\n",
    "poly.fit(X)\n",
    "X2 = poly.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   1.,   2.,   1.,   2.,   4.],\n",
       "       [  1.,   3.,   4.,   9.,  12.,  16.],\n",
       "       [  1.,   5.,   6.,  25.,  30.,  36.],\n",
       "       [  1.,   7.,   8.,  49.,  56.,  64.],\n",
       "       [  1.,   9.,  10.,  81.,  90., 100.]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X2 \n",
    "# 因为X有两个维度，polynomial features实际上是将X从0到2次方所有可能的组合都hstack起来了\n",
    "# 第一列为X的0次方， 第二列为X的第一个维度的1次方，第三列是X第二个维度的1次方，\n",
    "# 第四列是X的第一个维度的2次方，第六列是X第二个维度的2次方\n",
    "# 第五列是X的两个维度相乘的结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 如果degree=3的话将会出现更多的维度，原因和上面一样\n",
    "poly = PolynomialFeatures(degree=3)\n",
    "poly.fit(X)\n",
    "X3 = poly.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 10)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1.,    1.,    2.,    1.,    2.,    4.,    1.,    2.,    4.,\n",
       "           8.],\n",
       "       [   1.,    3.,    4.,    9.,   12.,   16.,   27.,   36.,   48.,\n",
       "          64.],\n",
       "       [   1.,    5.,    6.,   25.,   30.,   36.,  125.,  150.,  180.,\n",
       "         216.],\n",
       "       [   1.,    7.,    8.,   49.,   56.,   64.,  343.,  392.,  448.,\n",
       "         512.],\n",
       "       [   1.,    9.,   10.,   81.,   90.,  100.,  729.,  810.,  900.,\n",
       "        1000.]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X3"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "组合如下：\n",
    "\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.uniform(-3, 3, size=100)\n",
    "X = x.reshape(-1, 1)\n",
    "y = 0.5 * x**2 + x + 2 + np.random.normal(0, 1, size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# 管道的好处就在于可以直接指定每一步的类，由管道自动化执行，而不用手动敲打每一步的代码，通过管道，我们创建了一个多项式回归器\n",
    "poly_reg = Pipeline([\n",
    "                    ('poly', PolynomialFeatures(degree=2)),\n",
    "                    ('std_scaler', StandardScaler()),\n",
    "                    ('lin_reg', LinearRegression())\n",
    "                    ], verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Pipeline] .............. (step 1 of 3) Processing poly, total=   0.0s\n",
      "[Pipeline] ........ (step 2 of 3) Processing std_scaler, total=   0.0s\n",
      "[Pipeline] ........... (step 3 of 3) Processing lin_reg, total=   0.0s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('poly',\n",
       "                 PolynomialFeatures(degree=2, include_bias=True,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('std_scaler',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('lin_reg',\n",
       "                 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "                                  normalize=False))],\n",
       "         verbose=True)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predict = poly_reg.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f15be712810>]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(np.sort(x), y_predict[np.argsort(x)], color='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
